If $x = 2$ and $y = 5$, then what is the value of $\frac{x^4+2y^2}{6}$ ?
We have  \[\frac{x^4 + 2y^2}{6} = \frac{2^4 + 2(5^2)}{6} = \frac{16+2(25)}{6} = \frac{16+50}{6} = \frac{66}{6} = \boxed{11}.\]